Sharp Interface Level Set Method based CMFD Development : An Efficient Methodology on Non-Uniform Semi-Adaptive Mesh

Abstract

Focus of present work is to develop a new algorithm for multiphase flows to nearly replicate the hypothetical condition of Zero slope-Zero Error on Error-Computational Time plane or may be Negative slope-Zero Error condition in extreme cases. This may be executed by implementing tools like fast solvers, high performance computing, accurate multiphase modeling, grid strategy etc. However among all, grid generation being a most fundamental assumption of Computational Fluid Dynamics it is adopted as a base of present methodology. If we think intuitively then, in multiphase flow physics is very rich in the vicinity of interface. To capture such phenomenon grid near the interface should be very fine. Grid near the interface should be finer than the smallest length scale involved with interface. However away from the interface coarser grid would be sufficient. This particular idea can be implemented by employing grid strategies like grid clustering and stretching using transformation functions, multiblock grid and adaptive grid. In this title, methodology for non-uniform grid and semi-adaptive mesh is proposed. After which new grid type is proposed which is combination of non-uniform and semi-adaptive mesh. In present work Sharp Interface Level Set Method is used because of its more realistic formulation. Ghost Fluid Method based approach is implemented here to handle the jump in flow properties as well as jump in gradient of flow properties across the interface. To discretize governing equations obtained from volume and momentum conservation, Finite Volume Method (FVM) based formulation is implemented. However mass conservation equation is discretized using Finite Difference Method (FDM). In order to handle the control volume offset (because of staggering in control volumes of flow quantities) in stretched/clustered non-uniform grid, proper interpolation technique is developed. FDM based 3rd order accurate Essentially Non Oscillatory scheme is derived here for highly stretched non-uniform grid to prevent the mass dissipation. After using higher order schemes in discretizing spatial terms of mass conservation equation, temporal term also demands higher order discretization in order to have overall consistency. Hence ultimately mass conservation equation contributes significantly in overall computational time among other conservation equations. Based on this idea, Semi Adaptive Mesh Refinement (Semi AMR) strategy is proposed wherein single level adaption is done only for level set function while remaining flow properties are solved on fine grid itself. While developing Semi AMR strategy Quadtree data structure is used. In Semi AMR mesh ghost level set node are defined to handle unstructured node distribution. Along with it optimized node numbering is done using dynamic memory allocation to access node data. Combined non-uniform semi-adaptive mesh involves simultaneous implementation of methodology for non-uniform grid and Semi AMR. To demonstrate the fact that present methodology can closely mimic the Zero slope- Zero Error condition, performance study is carried out on various test problems. Problems includes Dam Break simulation, Droplet Coalescence, Jet Breakup problem, Rayleigh- Taylor instability, Droplet Impact on a Liquid Pool in the class of flows without phase change. Class of flows with phase change includes non-isothermal evaporation of droplet, solidification of under cooled liquid and non-isothermal evaporation of falling droplet.